Positronium ground state

so I had this thought earlier today. I am not claiming this is true or even likely but its interesting, possible (from everything I know), and may be testable by experiment.

What if annihilation doesnt actually exist? What if what we see as an electron annihilating with a positron is really just a positronium "atom" moving to the ground state? This "theory" has a lot of nice features so Im curious if its possible or not.

1) Dark matter: since leptons only experience the electromagnetic force, a positronium "atom" in the ground state should be completely invisible to us without exciting it. Im not 100% sure about this but from what I understand, in the ground state both the positron and the electron have spherically symmetric wave functions and overlap completely (not sure if the exclusion principle applies to different particles but if it does they would just have opposite spin). Therefore the "atom" would be electrically neutral at all points and therefore unable to detect without exciting. This could be a possible explanation of dark matter since its massive and undetectable.

2) No energy-mass conversions: When we send high energy photons into a vacuum we observe electron-positron pairs created. In this "theory", rather than being created from the photon, one of the particles absorbs the photon (which has energy greater than the ground state energy) and the "atom" is destroyed leaving an electron and positron.

3) No annihilation: Rather than electrons and positrons annihilating each other, they simple fall into the ground state of positronium and emit a photon.

4) Possibly testable: Since in any vacuum there would be a finite number of positronium "atoms", the behavior of pair creation would be different than if the pairs were actually created. Send x high energy photons into a vacuum and observe y electron-positron pairs created. Plotting x vs. y will give two very different graphs in the two cases. In the expected case it will be linear while in the case of my "theory", it will approach some maximum.

Like I said, Im sure there is some reason why this cant be true but I dont see it. I did check out the energy of the ground state of positronium which is 9.65e-30. The mass-energy of an electron, on the other hand, is 1.64e-13. There might be some way to reconcile that but either way it does dispute the theory (if they were identical it would be MUCH more convincing lol).

What if annihilation doesnt actually exist? What if what we see as an electron annihilating with a positron is really just a positronium "atom" moving to the ground state? This "theory" has a lot of nice features so Im curious if its possible or not.

Since we can detect the photons and neutrinos resulting from matter/antimatter annihilation, even when the particles have very small kinetic energy, where would this energy come from if the electron and positron remained in matter form?